Now my very long tooltip text doesn't have a linebreak, even though if I use alert(); it shows me that the text actually DOES have two lines. (It contains a "\" though, how do I remove that one by the way?)

This is not something that SVG 1.1 supports. SVG 1.2 does have the textArea element, with automatic word wrapping, but it's not implemented in all browsers. SVG 2 does not allow textArea. But it does have auto-wrapped text.

However, given that you already know where your linebreaks should occur, you can break your text into multiple <tspan>s, each with x="0" and dy="1.4em" to simulate actual lines of text. For example: